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3h
awarded  Good Question
1d
comment Computing irrational numbers
I should mention that most irrational numbers (i.e. all except a countable set) are not computable, one example being Chaitin's constant.
1d
accepted Integral involving Clausen function ${\large\int}_0^{2\pi}\operatorname{Cl}_2(x)^2\,x^p\,dx$
2d
awarded  Nice Question
May
21
comment Integral involving Clausen function ${\large\int}_0^{2\pi}\operatorname{Cl}_2(x)^2\,x^p\,dx$
My expression for $I(2)$ is accurate with at least 200 decimal digits of precision. I evaluated the integral both in Maple and Mathematica, and they returned exactly the same result.
May
21
accepted Integrals of the form ${\large\int}_0^\infty\operatorname{arccot}(x)\cdot\operatorname{arccot}(a\,x)\cdot\operatorname{arccot}(b\,x)\ dx$
May
21
revised Integral involving Clausen function ${\large\int}_0^{2\pi}\operatorname{Cl}_2(x)^2\,x^p\,dx$
added 62 characters in body
May
21
asked Integral involving Clausen function ${\large\int}_0^{2\pi}\operatorname{Cl}_2(x)^2\,x^p\,dx$
May
21
comment Do second-order categoricity proofs require a background concept of set?
In your answer you gave 2 examples (Suslin trees and existence of $0^\sharp$). At the first glance, it looks to me they can only be formalized in the second-order arithmentic, with quantification over sets of natural numbers. Am I wrong here? Can you give an example of a first-order arithmetic sentence that can have different truth-values in two models, despite they have the same natural numbers? Also, could you please explain what does it mean for a statements $\sigma$ to be non-standard?
May
20
comment Do second-order categoricity proofs require a background concept of set?
Very nice answer!
May
19
revised A curious equation containing an integral $\int_0^{\pi/4}\arctan\left(\tan^x\theta\right)d\theta=\frac{\ln2\cdot\ln x}{16}$
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May
19
revised A curious equation containing an integral $\int_0^{\pi/4}\arctan\left(\tan^x\theta\right)d\theta=\frac{\ln2\cdot\ln x}{16}$
added 183 characters in body
May
18
revised A curious equation containing an integral $\int_0^{\pi/4}\arctan\left(\tan^x\theta\right)d\theta=\frac{\ln2\cdot\ln x}{16}$
added 230 characters in body
May
18
comment A curious equation containing an integral $\int_0^{\pi/4}\arctan\left(\tan^x\theta\right)d\theta=\frac{\ln2\cdot\ln x}{16}$
@Farnight Inverse Symbolic Calculator: isc.carma.newcastle.edu.au
May
18
revised A curious equation containing an integral $\int_0^{\pi/4}\arctan\left(\tan^x\theta\right)d\theta=\frac{\ln2\cdot\ln x}{16}$
added 190 characters in body
May
18
answered A curious equation containing an integral $\int_0^{\pi/4}\arctan\left(\tan^x\theta\right)d\theta=\frac{\ln2\cdot\ln x}{16}$
May
18
reviewed Close Elementary statistics question (hypothesis test with accuracy of 5% and power of the test)
May
18
reviewed Close Combinations Lego Problem
May
18
reviewed Close Starting my nephew out on the journey to higher mathematics.
May
18
reviewed Close Binormal Probability